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Vector expressions

  1. Aug 16, 2016 #1
    1. The problem statement, all variables and given/known data

    let ##\vec{r}## be a vector from origin to the point (x,y,z) and let ##{\vec{r}\,}'## be a vector from the origin to the point (x',y',z'). Evaluate the following expressions

    ##1. \triangledown r ##

    ##2.\triangledown\frac{1}{r}##

    ##3.\triangledown\cdot r##

    ##4.\triangledown\times r##

    ##5.\triangledown^{2} r##

    ##6.\triangledown^{2} \frac{1}{r}##

    ##7.\triangledown\frac{1}{\mid\vec{r}-{\vec{r}\,}'\mid}##

    ##8.\triangledown\frac{1}{{\mid\vec{r}-{\vec{r}\,}'\mid}^2}##




    The attempt at a solution

    i have added my solution for the first few equations. My problem is page 3 and page 4. I cant get the right answer.
     

    Attached Files:

  2. jcsd
  3. Aug 16, 2016 #2

    BvU

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    Well, can you pick the one that's wrong ? 2 out of 3 say 3, so maybe the odd one out is the 'ccs'. What could be the problem here ?
     
  4. Aug 16, 2016 #3
    Yes my problem is ##3.\triangledown\cdot r## in C.c.s. I dont know how to get 3 as result like R.c.s which is the correct answer.
    and my solution for the S.c.s im not sure if its correct. Its seems wrong.
    I added the others so you can see how i solve the equations.
     
  5. Aug 16, 2016 #4

    BvU

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    Well, the expressions in your thread under

    2. Relevant equations

    don't help you much further at the moment :rolleyes:. I seem to remember quite different expressions for ##\nabla\cdot \vec A##. Could you check, e.g. here ?
     
  6. Aug 16, 2016 #5
    Thank you. You are great. I think i get it.
    I have uploaded an image with the solution. Sorry that i dont use Latex but im on mobile phone right now.
    Is this correct?
    image.jpeg
     
  7. Aug 16, 2016 #6

    BvU

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    Well done. A few more exercises are waiting ... :smile:
     
  8. Aug 16, 2016 #7
    thank you again. Than my solution for spherical is also wrong. ( on page 4)
     
  9. Aug 16, 2016 #8

    BvU

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    Indeed, the first two lines were some kind of inspiration ? After that, it looks pretty convincing !
     
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